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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.geometry.partitioning.utilities;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.util.Arrays;<a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.21"></a>
<FONT color="green">022</FONT>    <a name="line.22"></a>
<FONT color="green">023</FONT>    /** This class implements an ordering operation for T-uples.<a name="line.23"></a>
<FONT color="green">024</FONT>     *<a name="line.24"></a>
<FONT color="green">025</FONT>     * &lt;p&gt;Ordering is done by encoding all components of the T-uple into a<a name="line.25"></a>
<FONT color="green">026</FONT>     * single scalar value and using this value as the sorting<a name="line.26"></a>
<FONT color="green">027</FONT>     * key. Encoding is performed using the method invented by Georg<a name="line.27"></a>
<FONT color="green">028</FONT>     * Cantor in 1877 when he proved it was possible to establish a<a name="line.28"></a>
<FONT color="green">029</FONT>     * bijection between a line and a plane. The binary representations of<a name="line.29"></a>
<FONT color="green">030</FONT>     * the components of the T-uple are mixed together to form a single<a name="line.30"></a>
<FONT color="green">031</FONT>     * scalar. This means that the 2&lt;sup&gt;k&lt;/sup&gt; bit of component 0 is<a name="line.31"></a>
<FONT color="green">032</FONT>     * followed by the 2&lt;sup&gt;k&lt;/sup&gt; bit of component 1, then by the<a name="line.32"></a>
<FONT color="green">033</FONT>     * 2&lt;sup&gt;k&lt;/sup&gt; bit of component 2 up to the 2&lt;sup&gt;k&lt;/sup&gt; bit of<a name="line.33"></a>
<FONT color="green">034</FONT>     * component {@code t}, which is followed by the 2&lt;sup&gt;k-1&lt;/sup&gt;<a name="line.34"></a>
<FONT color="green">035</FONT>     * bit of component 0, followed by the 2&lt;sup&gt;k-1&lt;/sup&gt; bit of<a name="line.35"></a>
<FONT color="green">036</FONT>     * component 1 ... The binary representations are extended as needed<a name="line.36"></a>
<FONT color="green">037</FONT>     * to handle numbers with different scales and a suitable<a name="line.37"></a>
<FONT color="green">038</FONT>     * 2&lt;sup&gt;p&lt;/sup&gt; offset is added to the components in order to avoid<a name="line.38"></a>
<FONT color="green">039</FONT>     * negative numbers (this offset is adjusted as needed during the<a name="line.39"></a>
<FONT color="green">040</FONT>     * comparison operations).&lt;/p&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>     *<a name="line.41"></a>
<FONT color="green">042</FONT>     * &lt;p&gt;The more interesting property of the encoding method for our<a name="line.42"></a>
<FONT color="green">043</FONT>     * purpose is that it allows to select all the points that are in a<a name="line.43"></a>
<FONT color="green">044</FONT>     * given range. This is depicted in dimension 2 by the following<a name="line.44"></a>
<FONT color="green">045</FONT>     * picture:&lt;/p&gt;<a name="line.45"></a>
<FONT color="green">046</FONT>     *<a name="line.46"></a>
<FONT color="green">047</FONT>     * &lt;img src="doc-files/OrderedTuple.png" /&gt;<a name="line.47"></a>
<FONT color="green">048</FONT>     *<a name="line.48"></a>
<FONT color="green">049</FONT>     * &lt;p&gt;This picture shows a set of 100000 random 2-D pairs having their<a name="line.49"></a>
<FONT color="green">050</FONT>     * first component between -50 and +150 and their second component<a name="line.50"></a>
<FONT color="green">051</FONT>     * between -350 and +50. We wanted to extract all pairs having their<a name="line.51"></a>
<FONT color="green">052</FONT>     * first component between +30 and +70 and their second component<a name="line.52"></a>
<FONT color="green">053</FONT>     * between -120 and -30. We built the lower left point at coordinates<a name="line.53"></a>
<FONT color="green">054</FONT>     * (30, -120) and the upper right point at coordinates (70, -30). All<a name="line.54"></a>
<FONT color="green">055</FONT>     * points smaller than the lower left point are drawn in red and all<a name="line.55"></a>
<FONT color="green">056</FONT>     * points larger than the upper right point are drawn in blue. The<a name="line.56"></a>
<FONT color="green">057</FONT>     * green points are between the two limits. This picture shows that<a name="line.57"></a>
<FONT color="green">058</FONT>     * all the desired points are selected, along with spurious points. In<a name="line.58"></a>
<FONT color="green">059</FONT>     * this case, we get 15790 points, 4420 of which really belonging to<a name="line.59"></a>
<FONT color="green">060</FONT>     * the desired rectangle. It is possible to extract very small<a name="line.60"></a>
<FONT color="green">061</FONT>     * subsets. As an example extracting from the same 100000 points set<a name="line.61"></a>
<FONT color="green">062</FONT>     * the points having their first component between +30 and +31 and<a name="line.62"></a>
<FONT color="green">063</FONT>     * their second component between -91 and -90, we get a subset of 11<a name="line.63"></a>
<FONT color="green">064</FONT>     * points, 2 of which really belonging to the desired rectangle.&lt;/p&gt;<a name="line.64"></a>
<FONT color="green">065</FONT>     *<a name="line.65"></a>
<FONT color="green">066</FONT>     * &lt;p&gt;the previous selection technique can be applied in all<a name="line.66"></a>
<FONT color="green">067</FONT>     * dimensions, still using two points to define the interval. The<a name="line.67"></a>
<FONT color="green">068</FONT>     * first point will have all its components set to their lower bounds<a name="line.68"></a>
<FONT color="green">069</FONT>     * while the second point will have all its components set to their<a name="line.69"></a>
<FONT color="green">070</FONT>     * upper bounds.&lt;/p&gt;<a name="line.70"></a>
<FONT color="green">071</FONT>     *<a name="line.71"></a>
<FONT color="green">072</FONT>     * &lt;p&gt;T-uples with negative infinite or positive infinite components<a name="line.72"></a>
<FONT color="green">073</FONT>     * are sorted logically.&lt;/p&gt;<a name="line.73"></a>
<FONT color="green">074</FONT>     *<a name="line.74"></a>
<FONT color="green">075</FONT>     * &lt;p&gt;Since the specification of the {@code Comparator} interface<a name="line.75"></a>
<FONT color="green">076</FONT>     * allows only {@code ClassCastException} errors, some arbitrary<a name="line.76"></a>
<FONT color="green">077</FONT>     * choices have been made to handle specific cases. The rationale for<a name="line.77"></a>
<FONT color="green">078</FONT>     * these choices is to keep &lt;em&gt;regular&lt;/em&gt; and consistent T-uples<a name="line.78"></a>
<FONT color="green">079</FONT>     * together.&lt;/p&gt;<a name="line.79"></a>
<FONT color="green">080</FONT>     * &lt;ul&gt;<a name="line.80"></a>
<FONT color="green">081</FONT>     * &lt;li&gt;instances with different dimensions are sorted according to<a name="line.81"></a>
<FONT color="green">082</FONT>     * their dimension regardless of their components values&lt;/li&gt;<a name="line.82"></a>
<FONT color="green">083</FONT>     * &lt;li&gt;instances with {@code Double.NaN} components are sorted<a name="line.83"></a>
<FONT color="green">084</FONT>     * after all other ones (even after instances with positive infinite<a name="line.84"></a>
<FONT color="green">085</FONT>     * components&lt;/li&gt;<a name="line.85"></a>
<FONT color="green">086</FONT>     * &lt;li&gt;instances with both positive and negative infinite components<a name="line.86"></a>
<FONT color="green">087</FONT>     * are considered as if they had {@code Double.NaN}<a name="line.87"></a>
<FONT color="green">088</FONT>     * components&lt;/li&gt;<a name="line.88"></a>
<FONT color="green">089</FONT>     * &lt;/ul&gt;<a name="line.89"></a>
<FONT color="green">090</FONT>     *<a name="line.90"></a>
<FONT color="green">091</FONT>     * @version $Id: OrderedTuple.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.91"></a>
<FONT color="green">092</FONT>     * @since 3.0<a name="line.92"></a>
<FONT color="green">093</FONT>     */<a name="line.93"></a>
<FONT color="green">094</FONT>    public class OrderedTuple implements Comparable&lt;OrderedTuple&gt; {<a name="line.94"></a>
<FONT color="green">095</FONT>    <a name="line.95"></a>
<FONT color="green">096</FONT>        /** Sign bit mask. */<a name="line.96"></a>
<FONT color="green">097</FONT>        private static final long SIGN_MASK     = 0x8000000000000000L;<a name="line.97"></a>
<FONT color="green">098</FONT>    <a name="line.98"></a>
<FONT color="green">099</FONT>        /** Exponent bits mask. */<a name="line.99"></a>
<FONT color="green">100</FONT>        private static final long EXPONENT_MASK = 0x7ff0000000000000L;<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>        /** Mantissa bits mask. */<a name="line.102"></a>
<FONT color="green">103</FONT>        private static final long MANTISSA_MASK = 0x000fffffffffffffL;<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>        /** Implicit MSB for normalized numbers. */<a name="line.105"></a>
<FONT color="green">106</FONT>        private static final long IMPLICIT_ONE  = 0x0010000000000000L;<a name="line.106"></a>
<FONT color="green">107</FONT>    <a name="line.107"></a>
<FONT color="green">108</FONT>        /** Double components of the T-uple. */<a name="line.108"></a>
<FONT color="green">109</FONT>        private double[] components;<a name="line.109"></a>
<FONT color="green">110</FONT>    <a name="line.110"></a>
<FONT color="green">111</FONT>        /** Offset scale. */<a name="line.111"></a>
<FONT color="green">112</FONT>        private int offset;<a name="line.112"></a>
<FONT color="green">113</FONT>    <a name="line.113"></a>
<FONT color="green">114</FONT>        /** Least Significant Bit scale. */<a name="line.114"></a>
<FONT color="green">115</FONT>        private int lsb;<a name="line.115"></a>
<FONT color="green">116</FONT>    <a name="line.116"></a>
<FONT color="green">117</FONT>        /** Ordering encoding of the double components. */<a name="line.117"></a>
<FONT color="green">118</FONT>        private long[] encoding;<a name="line.118"></a>
<FONT color="green">119</FONT>    <a name="line.119"></a>
<FONT color="green">120</FONT>        /** Positive infinity marker. */<a name="line.120"></a>
<FONT color="green">121</FONT>        private boolean posInf;<a name="line.121"></a>
<FONT color="green">122</FONT>    <a name="line.122"></a>
<FONT color="green">123</FONT>        /** Negative infinity marker. */<a name="line.123"></a>
<FONT color="green">124</FONT>        private boolean negInf;<a name="line.124"></a>
<FONT color="green">125</FONT>    <a name="line.125"></a>
<FONT color="green">126</FONT>        /** Not A Number marker. */<a name="line.126"></a>
<FONT color="green">127</FONT>        private boolean nan;<a name="line.127"></a>
<FONT color="green">128</FONT>    <a name="line.128"></a>
<FONT color="green">129</FONT>        /** Build an ordered T-uple from its components.<a name="line.129"></a>
<FONT color="green">130</FONT>         * @param components double components of the T-uple<a name="line.130"></a>
<FONT color="green">131</FONT>         */<a name="line.131"></a>
<FONT color="green">132</FONT>        public OrderedTuple(final double ... components) {<a name="line.132"></a>
<FONT color="green">133</FONT>            this.components = components.clone();<a name="line.133"></a>
<FONT color="green">134</FONT>            int msb = Integer.MIN_VALUE;<a name="line.134"></a>
<FONT color="green">135</FONT>            lsb     = Integer.MAX_VALUE;<a name="line.135"></a>
<FONT color="green">136</FONT>            posInf  = false;<a name="line.136"></a>
<FONT color="green">137</FONT>            negInf  = false;<a name="line.137"></a>
<FONT color="green">138</FONT>            nan     = false;<a name="line.138"></a>
<FONT color="green">139</FONT>            for (int i = 0; i &lt; components.length; ++i) {<a name="line.139"></a>
<FONT color="green">140</FONT>                if (Double.isInfinite(components[i])) {<a name="line.140"></a>
<FONT color="green">141</FONT>                    if (components[i] &lt; 0) {<a name="line.141"></a>
<FONT color="green">142</FONT>                        negInf = true;<a name="line.142"></a>
<FONT color="green">143</FONT>                    } else {<a name="line.143"></a>
<FONT color="green">144</FONT>                        posInf = true;<a name="line.144"></a>
<FONT color="green">145</FONT>                    }<a name="line.145"></a>
<FONT color="green">146</FONT>                } else if (Double.isNaN(components[i])) {<a name="line.146"></a>
<FONT color="green">147</FONT>                    nan = true;<a name="line.147"></a>
<FONT color="green">148</FONT>                } else {<a name="line.148"></a>
<FONT color="green">149</FONT>                    final long b = Double.doubleToLongBits(components[i]);<a name="line.149"></a>
<FONT color="green">150</FONT>                    final long m = mantissa(b);<a name="line.150"></a>
<FONT color="green">151</FONT>                    if (m != 0) {<a name="line.151"></a>
<FONT color="green">152</FONT>                        final int e = exponent(b);<a name="line.152"></a>
<FONT color="green">153</FONT>                        msb = FastMath.max(msb, e + computeMSB(m));<a name="line.153"></a>
<FONT color="green">154</FONT>                        lsb = FastMath.min(lsb, e + computeLSB(m));<a name="line.154"></a>
<FONT color="green">155</FONT>                    }<a name="line.155"></a>
<FONT color="green">156</FONT>                }<a name="line.156"></a>
<FONT color="green">157</FONT>            }<a name="line.157"></a>
<FONT color="green">158</FONT>    <a name="line.158"></a>
<FONT color="green">159</FONT>            if (posInf &amp;&amp; negInf) {<a name="line.159"></a>
<FONT color="green">160</FONT>                // instance cannot be sorted logically<a name="line.160"></a>
<FONT color="green">161</FONT>                posInf = false;<a name="line.161"></a>
<FONT color="green">162</FONT>                negInf = false;<a name="line.162"></a>
<FONT color="green">163</FONT>                nan    = true;<a name="line.163"></a>
<FONT color="green">164</FONT>            }<a name="line.164"></a>
<FONT color="green">165</FONT>    <a name="line.165"></a>
<FONT color="green">166</FONT>            if (lsb &lt;= msb) {<a name="line.166"></a>
<FONT color="green">167</FONT>                // encode the T-upple with the specified offset<a name="line.167"></a>
<FONT color="green">168</FONT>                encode(msb + 16);<a name="line.168"></a>
<FONT color="green">169</FONT>            } else {<a name="line.169"></a>
<FONT color="green">170</FONT>                encoding = new long[] {<a name="line.170"></a>
<FONT color="green">171</FONT>                    0x0L<a name="line.171"></a>
<FONT color="green">172</FONT>                };<a name="line.172"></a>
<FONT color="green">173</FONT>            }<a name="line.173"></a>
<FONT color="green">174</FONT>    <a name="line.174"></a>
<FONT color="green">175</FONT>        }<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>        /** Encode the T-uple with a given offset.<a name="line.177"></a>
<FONT color="green">178</FONT>         * @param minOffset minimal scale of the offset to add to all<a name="line.178"></a>
<FONT color="green">179</FONT>         * components (must be greater than the MSBs of all components)<a name="line.179"></a>
<FONT color="green">180</FONT>         */<a name="line.180"></a>
<FONT color="green">181</FONT>        private void encode(final int minOffset) {<a name="line.181"></a>
<FONT color="green">182</FONT>    <a name="line.182"></a>
<FONT color="green">183</FONT>            // choose an offset with some margins<a name="line.183"></a>
<FONT color="green">184</FONT>            offset  = minOffset + 31;<a name="line.184"></a>
<FONT color="green">185</FONT>            offset -= offset % 32;<a name="line.185"></a>
<FONT color="green">186</FONT>    <a name="line.186"></a>
<FONT color="green">187</FONT>            if ((encoding != null) &amp;&amp; (encoding.length == 1) &amp;&amp; (encoding[0] == 0x0L)) {<a name="line.187"></a>
<FONT color="green">188</FONT>                // the components are all zeroes<a name="line.188"></a>
<FONT color="green">189</FONT>                return;<a name="line.189"></a>
<FONT color="green">190</FONT>            }<a name="line.190"></a>
<FONT color="green">191</FONT>    <a name="line.191"></a>
<FONT color="green">192</FONT>            // allocate an integer array to encode the components (we use only<a name="line.192"></a>
<FONT color="green">193</FONT>            // 63 bits per element because there is no unsigned long in Java)<a name="line.193"></a>
<FONT color="green">194</FONT>            final int neededBits  = offset + 1 - lsb;<a name="line.194"></a>
<FONT color="green">195</FONT>            final int neededLongs = (neededBits + 62) / 63;<a name="line.195"></a>
<FONT color="green">196</FONT>            encoding = new long[components.length * neededLongs];<a name="line.196"></a>
<FONT color="green">197</FONT>    <a name="line.197"></a>
<FONT color="green">198</FONT>            // mix the bits from all components<a name="line.198"></a>
<FONT color="green">199</FONT>            int  eIndex = 0;<a name="line.199"></a>
<FONT color="green">200</FONT>            int  shift  = 62;<a name="line.200"></a>
<FONT color="green">201</FONT>            long word   = 0x0L;<a name="line.201"></a>
<FONT color="green">202</FONT>            for (int k = offset; eIndex &lt; encoding.length; --k) {<a name="line.202"></a>
<FONT color="green">203</FONT>                for (int vIndex = 0; vIndex &lt; components.length; ++vIndex) {<a name="line.203"></a>
<FONT color="green">204</FONT>                    if (getBit(vIndex, k) != 0) {<a name="line.204"></a>
<FONT color="green">205</FONT>                        word |= 0x1L &lt;&lt; shift;<a name="line.205"></a>
<FONT color="green">206</FONT>                    }<a name="line.206"></a>
<FONT color="green">207</FONT>                    if (shift-- == 0) {<a name="line.207"></a>
<FONT color="green">208</FONT>                        encoding[eIndex++] = word;<a name="line.208"></a>
<FONT color="green">209</FONT>                        word  = 0x0L;<a name="line.209"></a>
<FONT color="green">210</FONT>                        shift = 62;<a name="line.210"></a>
<FONT color="green">211</FONT>                    }<a name="line.211"></a>
<FONT color="green">212</FONT>                }<a name="line.212"></a>
<FONT color="green">213</FONT>            }<a name="line.213"></a>
<FONT color="green">214</FONT>    <a name="line.214"></a>
<FONT color="green">215</FONT>        }<a name="line.215"></a>
<FONT color="green">216</FONT>    <a name="line.216"></a>
<FONT color="green">217</FONT>        /** Compares this ordered T-uple with the specified object.<a name="line.217"></a>
<FONT color="green">218</FONT>    <a name="line.218"></a>
<FONT color="green">219</FONT>         * &lt;p&gt;The ordering method is detailed in the general description of<a name="line.219"></a>
<FONT color="green">220</FONT>         * the class. Its main property is to be consistent with distance:<a name="line.220"></a>
<FONT color="green">221</FONT>         * geometrically close T-uples stay close to each other when stored<a name="line.221"></a>
<FONT color="green">222</FONT>         * in a sorted collection using this comparison method.&lt;/p&gt;<a name="line.222"></a>
<FONT color="green">223</FONT>    <a name="line.223"></a>
<FONT color="green">224</FONT>         * &lt;p&gt;T-uples with negative infinite, positive infinite are sorted<a name="line.224"></a>
<FONT color="green">225</FONT>         * logically.&lt;/p&gt;<a name="line.225"></a>
<FONT color="green">226</FONT>    <a name="line.226"></a>
<FONT color="green">227</FONT>         * &lt;p&gt;Some arbitrary choices have been made to handle specific<a name="line.227"></a>
<FONT color="green">228</FONT>         * cases. The rationale for these choices is to keep<a name="line.228"></a>
<FONT color="green">229</FONT>         * &lt;em&gt;normal&lt;/em&gt; and consistent T-uples together.&lt;/p&gt;<a name="line.229"></a>
<FONT color="green">230</FONT>         * &lt;ul&gt;<a name="line.230"></a>
<FONT color="green">231</FONT>         * &lt;li&gt;instances with different dimensions are sorted according to<a name="line.231"></a>
<FONT color="green">232</FONT>         * their dimension regardless of their components values&lt;/li&gt;<a name="line.232"></a>
<FONT color="green">233</FONT>         * &lt;li&gt;instances with {@code Double.NaN} components are sorted<a name="line.233"></a>
<FONT color="green">234</FONT>         * after all other ones (evan after instances with positive infinite<a name="line.234"></a>
<FONT color="green">235</FONT>         * components&lt;/li&gt;<a name="line.235"></a>
<FONT color="green">236</FONT>         * &lt;li&gt;instances with both positive and negative infinite components<a name="line.236"></a>
<FONT color="green">237</FONT>         * are considered as if they had {@code Double.NaN}<a name="line.237"></a>
<FONT color="green">238</FONT>         * components&lt;/li&gt;<a name="line.238"></a>
<FONT color="green">239</FONT>         * &lt;/ul&gt;<a name="line.239"></a>
<FONT color="green">240</FONT>    <a name="line.240"></a>
<FONT color="green">241</FONT>         * @param ot T-uple to compare instance with<a name="line.241"></a>
<FONT color="green">242</FONT>         * @return a negative integer if the instance is less than the<a name="line.242"></a>
<FONT color="green">243</FONT>         * object, zero if they are equal, or a positive integer if the<a name="line.243"></a>
<FONT color="green">244</FONT>         * instance is greater than the object<a name="line.244"></a>
<FONT color="green">245</FONT>    <a name="line.245"></a>
<FONT color="green">246</FONT>         */<a name="line.246"></a>
<FONT color="green">247</FONT>        public int compareTo(final OrderedTuple ot) {<a name="line.247"></a>
<FONT color="green">248</FONT>            if (components.length == ot.components.length) {<a name="line.248"></a>
<FONT color="green">249</FONT>                if (nan) {<a name="line.249"></a>
<FONT color="green">250</FONT>                    return +1;<a name="line.250"></a>
<FONT color="green">251</FONT>                } else if (ot.nan) {<a name="line.251"></a>
<FONT color="green">252</FONT>                    return -1;<a name="line.252"></a>
<FONT color="green">253</FONT>                } else if (negInf || ot.posInf) {<a name="line.253"></a>
<FONT color="green">254</FONT>                    return -1;<a name="line.254"></a>
<FONT color="green">255</FONT>                } else if (posInf || ot.negInf) {<a name="line.255"></a>
<FONT color="green">256</FONT>                    return +1;<a name="line.256"></a>
<FONT color="green">257</FONT>                } else {<a name="line.257"></a>
<FONT color="green">258</FONT>    <a name="line.258"></a>
<FONT color="green">259</FONT>                    if (offset &lt; ot.offset) {<a name="line.259"></a>
<FONT color="green">260</FONT>                        encode(ot.offset);<a name="line.260"></a>
<FONT color="green">261</FONT>                    } else if (offset &gt; ot.offset) {<a name="line.261"></a>
<FONT color="green">262</FONT>                        ot.encode(offset);<a name="line.262"></a>
<FONT color="green">263</FONT>                    }<a name="line.263"></a>
<FONT color="green">264</FONT>    <a name="line.264"></a>
<FONT color="green">265</FONT>                    final int limit = FastMath.min(encoding.length, ot.encoding.length);<a name="line.265"></a>
<FONT color="green">266</FONT>                    for (int i = 0; i &lt; limit; ++i) {<a name="line.266"></a>
<FONT color="green">267</FONT>                        if (encoding[i] &lt; ot.encoding[i]) {<a name="line.267"></a>
<FONT color="green">268</FONT>                            return -1;<a name="line.268"></a>
<FONT color="green">269</FONT>                        } else if (encoding[i] &gt; ot.encoding[i]) {<a name="line.269"></a>
<FONT color="green">270</FONT>                            return +1;<a name="line.270"></a>
<FONT color="green">271</FONT>                        }<a name="line.271"></a>
<FONT color="green">272</FONT>                    }<a name="line.272"></a>
<FONT color="green">273</FONT>    <a name="line.273"></a>
<FONT color="green">274</FONT>                    if (encoding.length &lt; ot.encoding.length) {<a name="line.274"></a>
<FONT color="green">275</FONT>                        return -1;<a name="line.275"></a>
<FONT color="green">276</FONT>                    } else if (encoding.length &gt; ot.encoding.length) {<a name="line.276"></a>
<FONT color="green">277</FONT>                        return +1;<a name="line.277"></a>
<FONT color="green">278</FONT>                    } else {<a name="line.278"></a>
<FONT color="green">279</FONT>                        return 0;<a name="line.279"></a>
<FONT color="green">280</FONT>                    }<a name="line.280"></a>
<FONT color="green">281</FONT>    <a name="line.281"></a>
<FONT color="green">282</FONT>                }<a name="line.282"></a>
<FONT color="green">283</FONT>            }<a name="line.283"></a>
<FONT color="green">284</FONT>    <a name="line.284"></a>
<FONT color="green">285</FONT>            return components.length - ot.components.length;<a name="line.285"></a>
<FONT color="green">286</FONT>    <a name="line.286"></a>
<FONT color="green">287</FONT>        }<a name="line.287"></a>
<FONT color="green">288</FONT>    <a name="line.288"></a>
<FONT color="green">289</FONT>        /** {@inheritDoc} */<a name="line.289"></a>
<FONT color="green">290</FONT>        @Override<a name="line.290"></a>
<FONT color="green">291</FONT>        public boolean equals(final Object other) {<a name="line.291"></a>
<FONT color="green">292</FONT>            if (this == other) {<a name="line.292"></a>
<FONT color="green">293</FONT>                return true;<a name="line.293"></a>
<FONT color="green">294</FONT>            } else if (other instanceof OrderedTuple) {<a name="line.294"></a>
<FONT color="green">295</FONT>                return compareTo((OrderedTuple) other) == 0;<a name="line.295"></a>
<FONT color="green">296</FONT>            } else {<a name="line.296"></a>
<FONT color="green">297</FONT>                return false;<a name="line.297"></a>
<FONT color="green">298</FONT>            }<a name="line.298"></a>
<FONT color="green">299</FONT>        }<a name="line.299"></a>
<FONT color="green">300</FONT>    <a name="line.300"></a>
<FONT color="green">301</FONT>        /** {@inheritDoc} */<a name="line.301"></a>
<FONT color="green">302</FONT>        @Override<a name="line.302"></a>
<FONT color="green">303</FONT>        public int hashCode() {<a name="line.303"></a>
<FONT color="green">304</FONT>            // the following constants are arbitrary small primes<a name="line.304"></a>
<FONT color="green">305</FONT>            final int multiplier = 37;<a name="line.305"></a>
<FONT color="green">306</FONT>            final int trueHash   = 97;<a name="line.306"></a>
<FONT color="green">307</FONT>            final int falseHash  = 71;<a name="line.307"></a>
<FONT color="green">308</FONT>    <a name="line.308"></a>
<FONT color="green">309</FONT>            // hash fields and combine them<a name="line.309"></a>
<FONT color="green">310</FONT>            // (we rely on the multiplier to have different combined weights<a name="line.310"></a>
<FONT color="green">311</FONT>            //  for all int fields and all boolean fields)<a name="line.311"></a>
<FONT color="green">312</FONT>            int hash = Arrays.hashCode(components);<a name="line.312"></a>
<FONT color="green">313</FONT>            hash = hash * multiplier + offset;<a name="line.313"></a>
<FONT color="green">314</FONT>            hash = hash * multiplier + lsb;<a name="line.314"></a>
<FONT color="green">315</FONT>            hash = hash * multiplier + (posInf ? trueHash : falseHash);<a name="line.315"></a>
<FONT color="green">316</FONT>            hash = hash * multiplier + (negInf ? trueHash : falseHash);<a name="line.316"></a>
<FONT color="green">317</FONT>            hash = hash * multiplier + (nan    ? trueHash : falseHash);<a name="line.317"></a>
<FONT color="green">318</FONT>    <a name="line.318"></a>
<FONT color="green">319</FONT>            return hash;<a name="line.319"></a>
<FONT color="green">320</FONT>    <a name="line.320"></a>
<FONT color="green">321</FONT>        }<a name="line.321"></a>
<FONT color="green">322</FONT>    <a name="line.322"></a>
<FONT color="green">323</FONT>        /** Get the components array.<a name="line.323"></a>
<FONT color="green">324</FONT>         * @return array containing the T-uple components<a name="line.324"></a>
<FONT color="green">325</FONT>         */<a name="line.325"></a>
<FONT color="green">326</FONT>        public double[] getComponents() {<a name="line.326"></a>
<FONT color="green">327</FONT>            return components.clone();<a name="line.327"></a>
<FONT color="green">328</FONT>        }<a name="line.328"></a>
<FONT color="green">329</FONT>    <a name="line.329"></a>
<FONT color="green">330</FONT>        /** Extract the sign from the bits of a double.<a name="line.330"></a>
<FONT color="green">331</FONT>         * @param bits binary representation of the double<a name="line.331"></a>
<FONT color="green">332</FONT>         * @return sign bit (zero if positive, non zero if negative)<a name="line.332"></a>
<FONT color="green">333</FONT>         */<a name="line.333"></a>
<FONT color="green">334</FONT>        private static long sign(final long bits) {<a name="line.334"></a>
<FONT color="green">335</FONT>            return bits &amp; SIGN_MASK;<a name="line.335"></a>
<FONT color="green">336</FONT>        }<a name="line.336"></a>
<FONT color="green">337</FONT>    <a name="line.337"></a>
<FONT color="green">338</FONT>        /** Extract the exponent from the bits of a double.<a name="line.338"></a>
<FONT color="green">339</FONT>         * @param bits binary representation of the double<a name="line.339"></a>
<FONT color="green">340</FONT>         * @return exponent<a name="line.340"></a>
<FONT color="green">341</FONT>         */<a name="line.341"></a>
<FONT color="green">342</FONT>        private static int exponent(final long bits) {<a name="line.342"></a>
<FONT color="green">343</FONT>            return ((int) ((bits &amp; EXPONENT_MASK) &gt;&gt; 52)) - 1075;<a name="line.343"></a>
<FONT color="green">344</FONT>        }<a name="line.344"></a>
<FONT color="green">345</FONT>    <a name="line.345"></a>
<FONT color="green">346</FONT>        /** Extract the mantissa from the bits of a double.<a name="line.346"></a>
<FONT color="green">347</FONT>         * @param bits binary representation of the double<a name="line.347"></a>
<FONT color="green">348</FONT>         * @return mantissa<a name="line.348"></a>
<FONT color="green">349</FONT>         */<a name="line.349"></a>
<FONT color="green">350</FONT>        private static long mantissa(final long bits) {<a name="line.350"></a>
<FONT color="green">351</FONT>            return ((bits &amp; EXPONENT_MASK) == 0) ?<a name="line.351"></a>
<FONT color="green">352</FONT>                   ((bits &amp; MANTISSA_MASK) &lt;&lt; 1) :          // subnormal number<a name="line.352"></a>
<FONT color="green">353</FONT>                   (IMPLICIT_ONE | (bits &amp; MANTISSA_MASK)); // normal number<a name="line.353"></a>
<FONT color="green">354</FONT>        }<a name="line.354"></a>
<FONT color="green">355</FONT>    <a name="line.355"></a>
<FONT color="green">356</FONT>        /** Compute the most significant bit of a long.<a name="line.356"></a>
<FONT color="green">357</FONT>         * @param l long from which the most significant bit is requested<a name="line.357"></a>
<FONT color="green">358</FONT>         * @return scale of the most significant bit of {@code l},<a name="line.358"></a>
<FONT color="green">359</FONT>         * or 0 if {@code l} is zero<a name="line.359"></a>
<FONT color="green">360</FONT>         * @see #computeLSB<a name="line.360"></a>
<FONT color="green">361</FONT>         */<a name="line.361"></a>
<FONT color="green">362</FONT>        private static int computeMSB(final long l) {<a name="line.362"></a>
<FONT color="green">363</FONT>    <a name="line.363"></a>
<FONT color="green">364</FONT>            long ll = l;<a name="line.364"></a>
<FONT color="green">365</FONT>            long mask  = 0xffffffffL;<a name="line.365"></a>
<FONT color="green">366</FONT>            int  scale = 32;<a name="line.366"></a>
<FONT color="green">367</FONT>            int  msb   = 0;<a name="line.367"></a>
<FONT color="green">368</FONT>    <a name="line.368"></a>
<FONT color="green">369</FONT>            while (scale != 0) {<a name="line.369"></a>
<FONT color="green">370</FONT>                if ((ll &amp; mask) != ll) {<a name="line.370"></a>
<FONT color="green">371</FONT>                    msb |= scale;<a name="line.371"></a>
<FONT color="green">372</FONT>                    ll = ll &gt;&gt; scale;<a name="line.372"></a>
<FONT color="green">373</FONT>                }<a name="line.373"></a>
<FONT color="green">374</FONT>                scale = scale &gt;&gt; 1;<a name="line.374"></a>
<FONT color="green">375</FONT>                mask  = mask &gt;&gt; scale;<a name="line.375"></a>
<FONT color="green">376</FONT>            }<a name="line.376"></a>
<FONT color="green">377</FONT>    <a name="line.377"></a>
<FONT color="green">378</FONT>            return msb;<a name="line.378"></a>
<FONT color="green">379</FONT>    <a name="line.379"></a>
<FONT color="green">380</FONT>        }<a name="line.380"></a>
<FONT color="green">381</FONT>    <a name="line.381"></a>
<FONT color="green">382</FONT>        /** Compute the least significant bit of a long.<a name="line.382"></a>
<FONT color="green">383</FONT>         * @param l long from which the least significant bit is requested<a name="line.383"></a>
<FONT color="green">384</FONT>         * @return scale of the least significant bit of {@code l},<a name="line.384"></a>
<FONT color="green">385</FONT>         * or 63 if {@code l} is zero<a name="line.385"></a>
<FONT color="green">386</FONT>         * @see #computeMSB<a name="line.386"></a>
<FONT color="green">387</FONT>         */<a name="line.387"></a>
<FONT color="green">388</FONT>        private static int computeLSB(final long l) {<a name="line.388"></a>
<FONT color="green">389</FONT>    <a name="line.389"></a>
<FONT color="green">390</FONT>            long ll = l;<a name="line.390"></a>
<FONT color="green">391</FONT>            long mask  = 0xffffffff00000000L;<a name="line.391"></a>
<FONT color="green">392</FONT>            int  scale = 32;<a name="line.392"></a>
<FONT color="green">393</FONT>            int  lsb   = 0;<a name="line.393"></a>
<FONT color="green">394</FONT>    <a name="line.394"></a>
<FONT color="green">395</FONT>            while (scale != 0) {<a name="line.395"></a>
<FONT color="green">396</FONT>                if ((ll &amp; mask) == ll) {<a name="line.396"></a>
<FONT color="green">397</FONT>                    lsb |= scale;<a name="line.397"></a>
<FONT color="green">398</FONT>                    ll = ll &gt;&gt; scale;<a name="line.398"></a>
<FONT color="green">399</FONT>                }<a name="line.399"></a>
<FONT color="green">400</FONT>                scale = scale &gt;&gt; 1;<a name="line.400"></a>
<FONT color="green">401</FONT>                mask  = mask &gt;&gt; scale;<a name="line.401"></a>
<FONT color="green">402</FONT>            }<a name="line.402"></a>
<FONT color="green">403</FONT>    <a name="line.403"></a>
<FONT color="green">404</FONT>            return lsb;<a name="line.404"></a>
<FONT color="green">405</FONT>    <a name="line.405"></a>
<FONT color="green">406</FONT>        }<a name="line.406"></a>
<FONT color="green">407</FONT>    <a name="line.407"></a>
<FONT color="green">408</FONT>        /** Get a bit from the mantissa of a double.<a name="line.408"></a>
<FONT color="green">409</FONT>         * @param i index of the component<a name="line.409"></a>
<FONT color="green">410</FONT>         * @param k scale of the requested bit<a name="line.410"></a>
<FONT color="green">411</FONT>         * @return the specified bit (either 0 or 1), after the offset has<a name="line.411"></a>
<FONT color="green">412</FONT>         * been added to the double<a name="line.412"></a>
<FONT color="green">413</FONT>         */<a name="line.413"></a>
<FONT color="green">414</FONT>        private int getBit(final int i, final int k) {<a name="line.414"></a>
<FONT color="green">415</FONT>            final long bits = Double.doubleToLongBits(components[i]);<a name="line.415"></a>
<FONT color="green">416</FONT>            final int e = exponent(bits);<a name="line.416"></a>
<FONT color="green">417</FONT>            if ((k &lt; e) || (k &gt; offset)) {<a name="line.417"></a>
<FONT color="green">418</FONT>                return 0;<a name="line.418"></a>
<FONT color="green">419</FONT>            } else if (k == offset) {<a name="line.419"></a>
<FONT color="green">420</FONT>                return (sign(bits) == 0L) ? 1 : 0;<a name="line.420"></a>
<FONT color="green">421</FONT>            } else if (k &gt; (e + 52)) {<a name="line.421"></a>
<FONT color="green">422</FONT>                return (sign(bits) == 0L) ? 0 : 1;<a name="line.422"></a>
<FONT color="green">423</FONT>            } else {<a name="line.423"></a>
<FONT color="green">424</FONT>                final long m = (sign(bits) == 0L) ? mantissa(bits) : -mantissa(bits);<a name="line.424"></a>
<FONT color="green">425</FONT>                return (int) ((m &gt;&gt; (k - e)) &amp; 0x1L);<a name="line.425"></a>
<FONT color="green">426</FONT>            }<a name="line.426"></a>
<FONT color="green">427</FONT>        }<a name="line.427"></a>
<FONT color="green">428</FONT>    <a name="line.428"></a>
<FONT color="green">429</FONT>    }<a name="line.429"></a>




























































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